Sounds like you might be forgetting to drop some stitches off your needle after you work them. That is a common mistake when first learning to knit. Or you may be doing a yarn-over between some stitches which adds stitches onto your needle. If you take a picture of your piece and post it here, someone may be able to look at it and help you figure out what you are doing wrong.

It could be a couple things. One is as Mary said you may not be knitting the stitch properly. Make sure after you wrap the yarn and pull it through that you slide the stitch off the needle. One stitch will remain. Watch the video at the tab at the top of the page. If you need still photos you can choose one of these -

Scroll down for still photos:continental (holding the working yarn in your left hand)english (holding the working yarn in your right hand)

You could also be doing accidental increases.

__________________
Jan

When asking questions ALWAYS post the name and a link for the pattern if you have it.

I did the same thing when I first started. There are a lot of ways the extra stitches can pop on there as MGM listed.

For me, I was a very loose knitter in the beginning and I kept thinking the yarn between stitches was a dropped stitch because of how loose it was so I would pick it up and knit it... eventually I figured out that I had NOT dropped any stitches and stopped doing that and it solved the issue.

Not sure if you are doing this but I thought I'd throw it out there.

Keep at it though. When I was knitting my first scarf I just kept knitting past every error. It was a TERRIBLE scarf but I was able to see my errors and improve on them. One end of the scarf was horribly loose, and oddly wide and thin and full of errors, and the other end showed more consistency with my stitches and was all one width and no mistakes.

my first idea would be:
count your stitches. If the number is the same as the cast on you are not adding stitches. Good thing, you shouldn't.

Then the question is: are you knitting the same tightness? you might be getting lose in your work. That could make all the difference. Are the stitches about the same "open and lose"? if so, that is not your problem so much, either (but it might be a minimal change from row to row.)

another frequent thing is: you might have done a very tight cast on. then the knitting is often more lose than the cast on and therefore the knitting flares out from the outer edge.
If that is your problem you would not get an increase in size anymore after you go a couple of inches further.
to fix that, though, I would pull it all out and cast on again (maybe with a different method? maybe with extra lose method (second needle)?)

Since I do not want to confuse you: I will give you tips on how to propperly fix the problem once you have identified the matter. Does any of the 3 things above happen?

- more stitches than in cast on?
- more and more lose knitting?
- flare after the cast on edge only?